We prove the existence of weak T-periodic solutions for a nonlinear mathematical model associated with suspension bridges. Under further assumptions a regularity result is also given.

In this paper we prove a maxmin principle for nonlinear nonoverdamped eigenvalue problems corresponding to the characterization of Courant, Fischer and Weyl for linear eigenproblems. We apply it to locate eigenvalues of a rational spectral problem in fluid-solid interaction.

A modal synthesis method to solve the elastoacoustic vibration problem is analyzed. A two-dimensional coupled fluid-solid system is considered; the solid is described by displacement variables, whereas displacement potential is used for the fluid. A particular modal synthesis leading to a symmetric eigenvalue problem is introduced. Finite element discretizations with lagrangian elements are considered for solving the uncoupled problems. Convergence for eigenvalues and eigenfunctions is proved, error...

A modal synthesis method to solve the elastoacoustic vibration problem is analyzed. A two-dimensional coupled fluid-solid system is considered; the solid is described by displacement variables, whereas displacement potential is used for the fluid. A particular modal synthesis leading to a symmetric eigenvalue problem is introduced. Finite element discretizations with Lagrangian elements are considered for solving the uncoupled problems. Convergence for eigenvalues and eigenfunctions is proved,...

In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as...

The operator $L_0:D_{L_0}\subset H\to H$, $L_{0}u=\frac{1}{r}\frac{d}{dr}\left\{r\frac{d}{dr}\left[\frac{1}{r}\frac{d}{dr}\left(r\frac{du}{dr}\right)\right]\right\}$, $D_{L_0}=\{u\in C^4\left([0,R]\right),u^{\text{'}}\left(0\right)=u^{\text{'}\text{'}\text{'}\text{'}}\left(0\right)=0,u\left(R\right)=u^{\text{'}}\left(R\right)=0\}$, $H=L_{2,r}(0,R)$ is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on $L_0$ (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types $L_{0}u=g$ and $u_{tt}+L_{0}u=g$, respectively.

Si risolve nella sua generalità il problema delle vibrazioni libere trasversali dei gusci sferici ortotropi ribassati, che in un precedente Lavoro era stato affrontato limitatamente al campo delle vibrazioni assialsimmetriche. L'integrazione delle equazioni del moto è conseguita per serie mediante particolari sviluppi, generabili grazie ad un'opportuna sostituzione di una delle variabili indipendenti.

A coupled finite/boundary element method to approximate the free vibration modes of an elastic structure containing an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of one of the most usual procedures in engineering practice: an added mass formulation, which is posed in terms of boundary integral equations. Piecewise linear continuous elements are used to discretize the solid displacements and the fluid-solid interface variables. Spectral...

A coupled finite/boundary element method to approximate the free vibration modes of an elastic structure containing an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of one of the most usual procedures in engineering practice: an added mass formulation, which is posed in terms of boundary integral equations. Piecewise linear continuous elements are used to discretize the solid displacements and the fluid-solid interface variables....